Question

Consider the automobile cruise-control system shown below: Engine ActuatorCarburetor 0.833 and load 40 3s +1 Compensator R(s)E(s) Ge(s) s +1 -t e(t) Sensor 0.03 1) Derive the closed-loop transfer function of V(s)/R(s) when Gc(s)-1 2) Derive the closed-loop transfer function of E(s)/R(s) when Ge(s)-1 3) Plot the time history of the error e(t) of the closed-loop system when r(t) is a unit step input. 4) Plot the root-loci of the uncompensated system (when Gc(s)-1). Mark the closed-loop complex poles on the figure. Find the time constant for the complex closed-loop poles Design a phase lead compensator with zero at (-2.0, 0) such that damping ratio of dominant poles is ζ-0.707 and the time constant is one-half that found in 4). Present details of the design. Use Matlab to automate the design process as much as you can, so it will be easier to carry out repeated task Derive the closed-loop transfer functions E(s)/R(s) and V(s)/R(s) for the compensated system. Calculate the closed-loop poles. Are the dominant ones at the desired locations? Plot the root-loci of the lead compensated system. Mark the position of desired dominant poles Plot the time history of the error e(t) of the lead-compensated system when r(t) is a unit step input. And compare the result with that of 3). Repeat 5) through 8) for the cases when the lead compensator's zero is at (-1.4, 0), (1.6, 0) (-1.8, 0), respectively. Explain the effect of the position of the zero on the system's response 5) 6) 7) 8) 9)

Answer 1

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